Vilmos Komornik’s research while affiliated with University of Strasbourg and other places

. We prove that under rather general assumptions an exactly controllable problem is uniformly stabilizable with arbitrarily prescribed decay rates. Our approach is direct and constructive and avoids many of the technical di#culties associated with the usual methods based on Riccati equations. We give several applications for the wave equation and for Petrovsky systems. Key words. observability, controllability, stabilizability by feedback, partial di#erential equation, wave equation, Petrovsky system AMS subject classifications. 35L05, 35Q72, 93B05, 93B07, 93C20, 93D15 PII. S0363012996301609 1. Introduction. Let# be a nonempty bounded open set in R n having a boundary # of class C 2 , and consider the following problem: (1.1) y ## -#y = 0 in# × (0, #), (1.2) y(0) = y 0 and y # (0) = y 1 in# , (1.3) y = u on # × (0, #). Considering u as a control function, a natural problem is to seek stabilizing feedback laws u = F (y, y # ). In order to motivate our work, let us r...